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This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-objective H2/H ∞ maximum power tracking control of a variable speed wind turbine to minimize the H2 tracking error and ensure the H ∞ model reference-tracking performance, simultaneously. The optimal condition is obtained via a boost converter use, which adapts the load impedance to the wind turbine generator. Thus, based on the fuzzy T-S model, a multi-objective Maximum Power Point Tracking (MPPT) controller is developed, ensuring maximum power transfer, despite wind speed variation and system uncertainty. To specify the optimal trajectory to follow, a TS reference model is proposed taking as input the optimal rectified DC current. The conditions of stability and stabilization are expressed in terms of linear matrix inequality (LMI) for uncertain and disturbed T-S models leading to determining the controller gains. Finally, an example of MPP tracking applied to a Wind Energy Conversion System (WECS) illustrates the effectiveness of the proposed fuzzy control law. [ABSTRACT FROM AUTHOR]

This paper investigates the non-fragile robust H ∞ control problem of nonlinear uncertain neutral stochastic Takagi–Sugeno (T–S) fuzzy systems with mixed time-delays. The uncertainties are norm-bounded and time-varying. Sufficient conditions for H ∞ performance analysis results of the delay-dependent condition is established via the Lyapunov–Krasovskii functional (LKF) technique and linear matrix inequality (LMI) method. Based on the H ∞ performance result, a desired fuzzy control is designed by solving LMIs. Finally, an example is provided to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Achieving the robust fixed‐time stabilization (FxTS) of uncertain reaction‐diffusion systems (RDSs) utilizing intermittent boundary control is a valuable and unresolved problem. This paper simultaneously considers the influence of the uncertainty of non‐diffusion and diffusion coefficients on RDSs and provides an effective solution for the treatment of the uncertainty of diffusion coefficient in the investigation of FxTS. Then, a fixed‐time control scheme is presented to stabilize uncertain RDSs within a fixed time, which incorporates the merits of intermittent and boundary control and reduces control costs in both the spatial and temporal domains. Besides, some sufficient conditions in the form of linear matrix inequalities are deduced to guarantee the robust FxTS of uncertain RDSs with Neumann and mixed boundary conditions, respectively, which contain and generalize some existing results. Finally, the validity of the intermittent boundary control scheme and the FxTS criteria developed in this paper are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

The stability and dynamic performance of the system are impacted by the uncertainties present in the converter model and controller parameters. This paper introduces a robust non-fragile control approach that addresses the influence of these uncertainties. The approach involves developing a control law that achieves quadratic stabilization of the closed-loop system while also satisfying the H∞ norm constraint for disturbance attenuation. Based on this concept, a robust non-fragile PI controller is designed explicitly for voltage mode control of a dc–dc buck converter. The effectiveness of the proposed control technique is evaluated from two perspectives: (i) its ability to withstand significant perturbations in plant parameters and load disturbances and (ii) its resilience in the presence of variations in controller parameters. The effectiveness of the proposed control scheme is validated using simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of finite-time observer-based H ∞ control design of networked switched systems (NSS) subject to external disturbances via an event-triggered observation strategy. This triggering strategy is used to decide when the output measurements are sent to the observer over the communication network. By incorporating digital networks, the closed-loop system is modeled as a switched delayed system due to network-induced delays. By using the average dwell time (ADT) switching method with the Lyapunov–Krasovskii functional, several sufficient linear matrix inequalities (LMIs) conditions for the observer-based control synthesis are developed to guarantee the finite-time boundedness and the disturbance attenuation control performance of the resulting switched delayed system. Finally, an example is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the boundary fixed-time stabilisation for delay reaction–diffusion systems (DRDSs). A new boundary controller is designed to achieve fixed time stability of DRDSs. Firstly, a boundary fixed-time controller is presented for DRDSs. Then based on the designed boundary controller, using Lyapunov functional method, fixed-time stability lemma and Poincaré's inequality, we obtain the criteria to guarantee the fixed-time stability of DRDSs. In addition, boundary fixed-time controller is proposed for uncertain DRDSs to reach robust fixed-time stability. Both the cases, the systems with or without uncertainties, are severally followed by a fixed time, which is an upper-bound of the settling time and irrelevant to the initial conditions. Finally, two simulation examples are given to illustrate the fixed-time stability of the controlled systems, which show the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the issue of simultaneous fault detection and control (SFDC) for a class of switched linear systems with input and state delays is being addressed. A detector/controller unit (dynamic observer/observer-based controller) is suggested for a residual generation that simultaneously takes into account the control and fault detection objectives using specific performance indices. It is assumed that the delay will fluctuate within a range with a lower bound that is not zero. Based on a Lyapunov–Krasovskii functional (LKF), and thanks to the free-weighting matrix and projection lemma, a new sufficient condition for developing a new method is put forth in terms of a set of linear matrix inequalities (LMIs). To illustrate how well the suggested results work, the proposed method is applied to a vehicle roll dynamic. [ABSTRACT FROM AUTHOR]

A robust global fuzzy sliding mode controller is designed in this paper for the synchronization of non-linear systems with control input non-linearities (CIN) and uncertainties. A consistent global fuzzy sliding mode control (GFSMC) law is developed, which guarantees the suppression of the reaching phase and the presence of the sliding phase from the initial time. Chattering phenomenon, which is characteristic of customary sliding mode control (SMC), avoided by the on-line fuzzy regulation of the sliding surface in the controller, when the system is subject to disturbances and CIN. Finite-time boundedness (FTB) properties are designed with adequate conditions, which are entrenched in terms of linear matrix inequalities (LMIs) with the help of cost and Lyapunov functions. Numerical simulations for the synchronization problem of the chaotic modified Colpitt's system and Duffing system clearly show the good performance of the proposed control scheme. The present work provides a regular procedure to design GFSMC for a class of non-linear systems with CIN. [ABSTRACT FROM AUTHOR]

The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method. [ABSTRACT FROM AUTHOR]

In this paper, the desired yaw orientation for an autonomous underwater vehicle is attained by acquiring a cascaded control structure based on a robust optimal control algorithm with a backstepping approach. A robust state feedback optimal control law is designed to control the yaw rate. Hence, the desired yaw rate is intended to be obtained by the backstepping controller by controlling the desired yaw orientation. The implementation of the proposed robust control algorithm is formulated by using semi-definite programming. A linear quadratic regulator in terms of linear matrix inequality is designed to address the control problem. The design of robust optimal control law in the steering plane is achieved by considering an uncertain polytopic AUV system. Realization of the proposed control algorithm is conducted in MATLAB/Simulink environment using the YALMIP tool. Robust behavior is ensured by the proposed control algorithm while tracking the desired yaw. The robustness analysis is extended by considering the various ranges of specific uncertain parameters to highlight the efficacies of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

The aim of this work is the design of a current control by means of state feedback, based on linear matrix inequalities (LMI), and it is applied in a DC-DC coupled inductors Buck-Boost modular converter, which has been widely used in distributed generation systems with renewable energy sources. This method considers constraints on the location of poles defined in the complex plane called d-stability. The closed-loop control system is implemented in Matlab® Simulink and validated under different test scenarios, where better dynamic performance is obtained, its operating range is extended, with shorter settling times and a better time-response, in contrast with the classical PI control technique. [ABSTRACT FROM AUTHOR]

Low-frequency oscillations (LFOs) pose a significant obstacle in achieving optimal power flow and utilizing transmission corridors in large interconnected power systems. In this study, linear matrix inequality (LMI) base robust H ∞ wide-area damping controller (WADC) is introduced to effectively address critical LFOs. The proposed WADC utilizes wide-area signals, which modulate the phase angle of a thyristor-controlled phase shifter device. To ensure that the concerned modes of LFOs lie in left half of the complex plane, a D-space sub-region approach is applied. However, using wide-area signals introduces time delays, which negatively impact the efficacy of the WADC; hence, a time delay compensator (TDC) is incorporated into the feedback path of the signals. The proposed approach involves four key steps: selecting feedback signals using a combined modal transformation and geometric approach, designing an appropriate TDC, building a generalized plant with mixed sensitivity weights, and solving the LMI. The dynamic efficacy is verified on IEEE 4-machine 11-bus system, and 10-machine 39-bus system. Poorly damped single and multiple critical modes are placed in the D-space region of interest with specified damping ratios viz. 10% and 15%. Furthermore, damping ratios of critical modes are maintained with TDC based proposed WADC while deteriorating with other counterparts. [ABSTRACT FROM AUTHOR]

The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method. [ABSTRACT FROM AUTHOR]

System stability deterioration in microgrids commonly occurs due to unpredictable faults and equipment malfunctions. Recently, robust control techniques have been used in microgrid systems to address these difficulties. In this paper, for DC-islanded microgrids that have sensors faults, a new passive fault-tolerant control strategy is developed. The suggested approach can be used to maintain system stability in the presence of flaws, such as faulty actuators and sensors, as well as component failures. The suggested control is effective when the fault is never recognized (or when the fault is not being precisely known, and some ambiguity in the fault may be interpreted as uncertainty in the system's dynamics following the fault). The design is built around a derived sufficient condition in the context of linear matrix inequalities (LMIs) and the attractive ellipsoid technique. The ellipsoidal stabilization idea is to bring the state trajectories into a small region including the origin (an ellipsoid with minimum volume) and the trajectories will not leave the ellipsoid for the future time. Finally, computational studies on a DC microgrid system are carried out to assess the effectiveness of the proposed fault-tolerant control approach. When compared with previous studies, the simulation results demonstrate that the proposed control technique can significantly enhance the reliability and efficiency of DC microgrid systems. [ABSTRACT FROM AUTHOR]

This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ0, generalized H2, and H∞ norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together. [ABSTRACT FROM AUTHOR]

This article proposes a new co‐design adaptive event‐triggered (AET) robust control method based on output feedback to stabilize nonlinear systems with parametric uncertainties. The proposed event‐triggered mechanism (ETM) is obtained based on the finite gain L2$$ {L}_2 $$ stability. First, in the case of pre‐designed control gains, an AET robust controller is designed to guarantee the stability of the closed‐loop system. Then, a new approach is presented to co‐design the control gain and the adaptive event‐triggered mechanism, simultaneously. The proposed ETM which is presented in the form of linear matrix inequalities, leads to an increase in the average of inter‐event times. Moreover, the stability in the presence of the event‐based system and avoidance of the Zeno phenomenon have been ensured. Finally, to indicate the capability of the proposed methods, two examples are simulated. Simulation results show that in the proposed method the feasibility margin and the quality of the response are well maintained, and the number of samplings is reduced. [ABSTRACT FROM AUTHOR]

This research examines new methods for stabilizing linear time-delay systems that are subject to denial-of-service (DoS) attacks. The study takes into account the different effects that a DoS attack can have on the system, specifically delay-independent and -dependent behaviour. The traditional proportional-integral-derivative (PID) acts on the error signal, which is the difference between the reference input and the measured output. The approach in this paper uses what we call the PID state feedback strategy, where the controller acts on the state signal. Our proposed strategy uses the Lyapunov–Krasovskii functional (LKF) to develop new linear matrix inequalities (LMIs). The study considers two scenarios where the time delay is either a continuous bounded function or a differentiable and time-varying function that falls within certain bounds. In both cases, new LMIs are derived to find the PID-like state feedback gains that will ensure robust stabilization. The findings are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

Summary: This article is concerned with the problem of robust fuzzy fault tolerant control for the nonlinear active suspension system via adaptive hybrid triggered scheme. To describe the system with high nonlinearity, a Takagi‐Sugeno fuzzy approach is applied by weighting a series of linear subsystems. During the design of the controller, the actuator failure is taken into consideration. To ease the network communication pressure, a novel adaptive hybrid triggered scheme is proposed for the suspension system. By applying a Bessel‐Legendre inequality and a Jensen's inequality together, the control algorithm can be derived in the form of linear matrix inequalities with less conservatism. Finally, compared with the existing sampled‐data H∞$$ {H}_{\infty } $$ control and adaptive event triggered H∞$$ {H}_{\infty } $$ control, numerical simulations are performed to demonstrate the effectiveness and superiority of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper studies several problems related to quadratic matrix inequalities (QMIs), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, or bounded or has a nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of "structured"" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMIs can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller and also leads to explicit formulas for data-guided feedback gains. [ABSTRACT FROM AUTHOR]

This work proposes a dimmable high-power factor LED driver operating from universal mains voltage range (90–264 V). In order to ensure stability and good dynamic response, for all operating points, a robust state feedback controller is used. Additionally, a H ∞ optimization is employed to attenuate the undesired output current low-frequency ripple. The controller's design is carried out by means of linear matrix inequalities (LMIs). In order to validate the theoretical analysis, a 34 W integrated off-line buck–boost flyback converter prototype was built. The results have shown the capability of the control scheme of ensuring robust stability and performance throughout the whole operating range, as well as providing an output current ripple attenuation of about 66%. [ABSTRACT FROM AUTHOR]

• The preview tracking controller for interconnected continuous-time systems with parameter uncertainties is designed. • The previewable information is integrated to the states of error system, which is a new framework of preview control. • The performance index function and performance signal are constructed to research the influence of disturbance. • The proposed preview controller can make the tracking quality improves as the preview length increases. This paper designs a decentralized robust preview tracking controller for interconnected continuous-time systems with parametric uncertainties. The uncertain error system, which is composed of the derivative equation of the states, the tracking error dynamics, and the available future reference dynamics, is constructed. Then, a cost function is introduced to evaluate the tracking quality. Meanwhile, a performance signal is defined to discuss the influence of disturbances on the tracking performance. Based on the above operations, the considered tracking control is converted to the H-infinity control of the uncertain error system. The sufficient conditions which guarantee that the closed-loop system is asymptotically stable with H-infinity disturbance attenuation are derived. Further, the decentralized preview controller is obtained with the help of the linear matrix inequality (LMI). The result is applied to double-parallel inverted pendulum system and 3-interconnected machine power system. Numerical simulation demonstrate that the suggested preview controller can make the output track the reference signal, and the tracking quality be improved as the preview length increases. [ABSTRACT FROM AUTHOR]

Most studies on a multiobjective optimal control problem (MOCP) with nonlinear stochastic jump‐diffusion system (NSJDS) constraints assume the state vector is available, but in practice, this is not necessarily the case. The observer‐based MOCP is worthy of further research. Furthermore, the hybrid multiobjective differential evolution algorithm (HMODEA) is usually employed to help solve MOCPs with dynamical system constraints, and such problems often have a higher computational burden. To address these two issues, a grid‐based front‐squeezing searching algorithm (GBFSA) is proposed to solve the observer‐based MOCP with NSJDS. Takagi‐Sugeno (T‐S) fuzzy model is used to approximate the NSJDS and convert the problem into an MOCP with linear matrix inequality (LMI) constraints. Then, the GBFSA efficiently searches for the Pareto front by merging the LMIs and the squeezing theorem. To automatically select a preferred Pareto controller, the minimum Manhattan distance (MMD) approch is applied. Mathematical proofs are given to show that the obtained Pareto optimal controller can concurrently stabilize the associated NSJDS and achieve the desired performance indices. In addition, computational complexity and convergence analysis are also provided. [ABSTRACT FROM AUTHOR]

This paper deals with the nonfragile fuzzy tracking control technique of a spacecraft subject to external disturbances and control gain uncertainties. First, the Takagi–Sugeno (T–S) fuzzy model of the tracking error dynamics is newly derived. Unlike the existing studies, we assume that the controller output is norm bounded and its gain matrix is perturbed because of the aging of the actuator. Next, a fuzzy disturbance observer (DOB) estimating the external disturbance is constructed to enhance the robustness of the control system. Then, a fuzzy controller feeding back the estimated disturbance is designed to attenuate external disturbances. In addition, we establish the linear matrix inequality (LMI) conditions, by which both the H ∞ disturbance attenuating performance and the asymptotic stabilization are guaranteed. From the solution to the LMI conditions, we obtain the controller and DOB gain matrices. Finally, a simulation example validates the disturbance estimation and tracking performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a robust guaranteed-cost controller for a half-vehicle active suspension system (HVASS) where the controller is subject to stochastic gain fluctuations. This randomly occurring uncertainty is a result of the imperfect implementation of the controller as well as the aging of the components. In this approach, the state-feedback controller is represented via multiple gains orchestrated by a Markovian process, and then an optimal multi-mode design approach with H2 norm constraints is considered to ensure system's asymptotic stability with a prescribed disturbance attenuation level. This design is based on Lyapunov theory and the controller is realized via a set of linear matrix inequalities. Compared to the existing works, the design is more reliable for practical HVASSs and is directly reducible to systems with perfectly implemented controllers. Simulation results and comparisons demonstrate the applicability and potentials of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses a non-fragile robust model predictive control design for a class of continuous-time uncertain systems with multiple state-delay and constrained control signals. The parameters of the system and the control gain are assumed to have perturbation in the additive form. The Lyapunov–Krasovskii functional approach is employed to derive sufficient conditions for determining a non-fragile robust state-feedback controller for all admissible uncertainties by minimising the upper bound of the defined quadratic cost function with respect to some linear matrix inequalities (LMIs). An additional inequality condition is imposed to address the constraint associated with the control signals. Numerical simulations are provided to assess the performance of the proposed controller. [ABSTRACT FROM AUTHOR]

This article proposes a robust inertial controller for converter-based distributed generators employed in low-inertia power systems like microgrids. The increasing penetration level of renewable energy sources based on power electronics converters in modern power systems reduces the inertial features of the system. It also increases concerns associated with the system uncertainty and sensitivity against disturbances. To cope with these challenges, by employing the proposed linear matrix inequality (LMI)-based mixed H 2 / H ∞ robust method, an optimal robust controller aided for inertial support as well as fast frequency restoration is provided. Using the proposed solution not only presents a better inertial response but also proposes a faster frequency restoration, by which the system's frequency can be restored immediately following any disturbance, even in the presence of system uncertainties. Through in-detailed frequency response analysis and time-domain simulations for different scenarios, it is illustrated that the proposed mechanism can be successfully employed to address the inertial requirements in power electronic-based power systems. In addition, the proposed LMI-based mixed H 2 / H ∞ control solution is compared with a number of other solutions to illustrate its better performance against disturbances. Simulation results validate the merits and effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, the design problem of Gain‐Scheduled Output‐Feedback (GSOF) controllers using inexact scheduling parameters for morphing aircraft during the wing transition process is addressed. Both the stability of the closed‐loop system and the L2 gain performance can be guaranteed under the controller based on measured (not actual) scheduling parameters. Firstly, the linear parameter‐varying (LPV) model of morphing aircraft is established by Jacobian linearization and the additive uncertainty is introduced into the scheduling parameters. By employing non‐linear transformations, the problem is formulated as the solution to a set of parameter‐dependent linear matrix inequalities (LMI) with a single‐line search parameter. Finally, the robustness of the flight control system to the wing transition process is verified under the condition of both the uncertainty of aerodynamic parameters and of scheduling parameters. [ABSTRACT FROM AUTHOR]

This research focuses on designing a min–max robust control based on a neural dynamic programming approach using a class of continuous differential neural networks (DNNs). The proposed controller solves the robust optimization of a proposed cost function that depends on the trajectories of a system with an uncertain mathematical model satisfying a class of non-linear perturbed systems. The dynamic programming min–max formulation enables robust control concerning bounded modelling uncertainties and disturbances. The Hamilton–Jacobi–Bellman (HJB) equation's value function, approximated by a DNN, permits to estimate the closed-loop formulation of the controller. The controller design is based on an estimated state trajectory with the worst possible uncertainties/perturbations that provide the degree of robustness using the proposed controller. The class of learning laws for the time-varying weights in the DNN is produced by studying the HJB partial differential equation. The controller uses the solution of the obtained learning laws and a time-varying Riccati equation. A recurrent algorithm based on the Kiefer–Wolfowitz method leads to adjusting the initial conditions for the weights to satisfy the final condition of the given cost function. The robust control suggested in this work is evaluated using a numerical example confirming the optimizing solution based on the DNN approximate for Bellman's value function. [ABSTRACT FROM AUTHOR]

This paper presents a design framework to obtain a robust multivariable Proportional-Integral-Derivative (PID) controller for second-order linear vibrating systems. A Proportional-Integral-Derivative plus acceleration (PIDA) controller is also proposed to deal with the regularization problem. Relevant control challenges, such as modeling error, regulatory performance optimization, regional pole placement, saturation avoidance, and constant reference tracking are handled within the proposed Linear Matrix Inequality (LMI) design approach. The design strategy is obtained from a linear transformation that can be applied to achieve constant reference tracking for an actuated subspace of underactuated systems. Moreover, the integral action has two additional objectives: (1) to improve regulatory performance in the presence of constant disturbance and (2) to increase the design degree of freedom in order to robustly achieve closed-loop specifications. Three simulation case studies are used to highlight the benefits of the PID and PIDA controllers. [ABSTRACT FROM AUTHOR]

Few studies have addressed the robustness of flexible spacecraft (FS) systems in the presence of input magnitudes and rate saturations. Thus, the present work is conducted to provide more information in this field and to propose a linear matrix inequality (LMI)-based H8 controller for a class of flexible spacecraft systems described by the two nonlinear dynamic models. First, a standard state-space representation is obtained by analyzing the characteristics of the rotation angle. Then, based on the assumption that the input constraints are negligible, a sufficient condition is derived by applying the definition of the H8 controller and exponential stability. In addition, a constrained controller is developed to ensure the saturation of the input magnitude and rate using an invariant set. Finally, two simulations with various conditions are carried out to evaluate the performance of the proposed methodology. [ABSTRACT FROM AUTHOR]

To improve the anti-disturbance stability of the autonomous underwater vehicles (AUVs) under bounded disturbances in amplitude, we develop a robust controller based on the estimated signals generated by the filter. The AUV studied has the characteristics of time-varying delay, under-actuated, and switched linear parameter varying (LPV) dynamics. Both the filter and the control strategies, we proposed are based on the robust L 1 performance criterion, which is suitable for the amplitude-bounded disturbances in the ocean environment. In the filter and controller design, the corresponding Lyapunov–Krasovskii functional is established to verify the stability of the systems. As there exist couplings between the designed functional and the system parameter matrices, slack matrices are constructed for decouplings after validating the stability of the under-actuated AUV filtering error system and closed-loop control system. The filter and the controller are obtained in the form of parameter linear matrix inequalities (PLMIs), whose solution is infinite-dimensional matrix inequalities. The approximate basis function and gridding technique are applied to transform the filter and the controller into that of finite dimensional LMIs. The simulation has verified the effectiveness of the robust L 1 filter and anti-disturbance depth robust L 1 controller. [ABSTRACT FROM AUTHOR]

This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results. [ABSTRACT FROM AUTHOR]

This paper presents the design of robust hierarchical control for homogeneous linear multi-agent systems (MAS) subject to parametric uncertainty and external disturbance. Specifically, the control design is based on a two-layer hierarchical structure consisting of an upper layer and a lower layer. In the lower layer, each agent is represented by a linear time-invariant system and executes a local action. Moreover, each agent exchanges information with neighbouring agents in the upper layer through an undirected graph to achieve the global goal of stabilisation and disturbance attenuation for the MAS. We propose two robust control designs, namely, robust H ∞ hierarchical control and robust H 2 hierarchical control. The design of local and global feedback control laws is formulated as a constrained optimisation over linear matrix inequalities (LMI). The LMI formulation can effectively incorporate the design objective to minimise disturbance attenuation. Numerical results show that the proposed robust controls ensure robust stability of MAS and outperform the existing nominal controls by improving the disturbance attenuation. [ABSTRACT FROM AUTHOR]

This article proposes a solution to the output regulation problem for uncertain linear systems with input saturation, state constraints, and external disturbances. The proposed robust control is composed of a linear and a nonlinear part. Each part of the control can be designed independently due to the use of an integral sliding‐mode control approach. The linear control, whose design is based on the barrier Lyapunov function and the attractive ellipsoid method, considers the input saturation, the state constraints, and the parameter uncertainties. The nonlinear part is based on an integral sliding‐mode control approach and it can compensate the effect of some matched disturbances. Also, a safe set where the system trajectories do not transgress the state constraints and input saturation, is provided. The proposed scheme guarantees asymptotic convergence to zero of the output regulation error coping with the system constraints and disturbances. A constructive and simple method, based on linear matrix inequalities, is proposed to compute the controller gains. Some simulation results illustrate the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents the design of a robust Restricted-Model-Based control providing tools for both stability and performance analysis of a class of Single-Input-Single-Output (SISO) Takagi–Sugeno (T–S) systems. The proposed method is evaluated in terms of induced L 2 -gain (or so-called H ∞ norm) to be robust to disturbances, sensor noises and uncertainties on the premise variables. Unlike the common approaches reported in the literature that consider exact premise variables, this work deals with the problem of unmeasured premises. The main results of this paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parametrised sets of linear matrix inequalities (LMIs). The proof of stability is based on the non-linear sector approach of the closed loop under Lyapunov conditions, L 2 norm and system transformations. The result is a control structure with only one parameter tuned via simple conditions. The performance and applicability of the proposed approach are illustrated through numerical simulations of an academic example. [ABSTRACT FROM AUTHOR]

An improved robust predictive control method is proposed for a class of multicellular descriptive LPV systems with bounded state disturbances, and an output feedback controller is designed to ensure the asymptotic stability of the systems. To offset the bounded state disturbance, the controller considered the undisturbed LPV system, and based on the off-line state observer, the linear matrix inequality is used to solve the minimum-maximum optimization problem in the infinite time domain of predictive control. Then the off-line state observer is adopted to obtain the difference between the estimated values of the disturbed LPV system and the undisturbed LPV system, and the feedback gain of the guaranteed performance is determined, so as to obtain the optimal offset that makes the disturbed LPV system asymptotically stable, which is combined with the undisturbed system control law as the optimal control law and applied to the actual system. The experimental results show that the improved robust predictive control method can obtain better control performance, and improve the stability of the system and the efficiency of solving optimization problems. The simulation experiments verifies the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• A resilient GESO based MRC control is designed to tackle the uncertainties and disturbances of turbofan systems. • The concise design of the control is developed by imposing the estimated disturbance on the control input channel. • The developed controller makes the state of the system to follow the given reference signal with accurate tracking. • Additive and multiplicative fluctuations are considered while designing the controller for better tracking performance. • The design procedure of the controller gain matrices are developed in the framework of linear matrix inequalities. The intention of this work is to analyse the issues of multiple disturbance estimation and rejection as well as robust tracking control design for turbofan systems subject to input gain perturbations. A standard generalized extended state observer is developed to estimate both the state disturbances and output measurement disturbances, simultaneously. Therewith, a modified repetitive controller is utilized with generalized extended state observer to track the states of the turbofan system accurately. Then, a new composite control strategy is developed by incorporating the estimates obtained via generalized extended state observer in modified repetitive controller to attenuate the effect of disturbances. Based on the pole placement technique, the observer gain is calculated and in accordance with Lyapunov stability theory, a set of sufficient conditions which ensures the robust asymptotic stability of the considered turbofan system is derived in the form of linear matrix inequalities. Moreover by offering the numerical examples with simulation results, the superiority of developed control strategy is validated. [ABSTRACT FROM AUTHOR]

A dual-loop robust control scheme and its property of performance separation are presented in this article. The dual-loop control scheme consists of two degrees of freedom for nominal and robust performances, with the nominal controller being any stabilizing controller in the observer-based state-feedback form and robust controller being a standard $H_{\infty }$ controller. When there is model error and/or disturbance, the robust controller is activated to compensate the nominal controller; otherwise, the dual-loop control returns to a single-loop nominal controller. We also show that the nominal and robust performances of the dual-loop control are independent of one another. As a result, the nominal and robust controllers can be designed separately offline, and then, online coordinated in the dual-loop control. Furthermore, the state-space realization and controller implementation are also provided. Finally, a two-wheeled robot with varying slip effect is considered as an illustrative example. Both simulation and experimental results show that the dual-loop control outperforms the classical robust control methods. [ABSTRACT FROM AUTHOR]

The paper is devoted to the synthesis, comparison, and optimization of robust LMI-control systems for the vertical plasma position in a D-shaped tokamak, specifically the T-15MD tokamak (Kurchatov Institute, Moscow, Russia). The novelty of this work is to find out the possibilities of LMI robust control systems, according to the criteria of the robust stability radius and control power peak at the rejection of a minor disruption type disturbance and a reference step signal using a unique unstable first-order plasma model. The plant under control consists of the connected in series plasma model with additive disturbance containing plant uncertainties, horizontal field coil (HFC), and actuator model as a multiphase rectifier. A set of robust controllers was designed by Linear Matrix Inequalities (LMI) method with pole placement in the LMI regions, state H2/H∞ performance, and output signal performance. The LMI theorems of the paper are directed to design the robust controllers and study the systems with the aim of eliminating the gap between theory and practice. The main achievement of this work consists in the optimization of robust control systems of the unstable plant with uncertain disturbance on the set of LMI synthesis approaches. The control systems have original quality criteria, such as control power and robust stability radius. The best control system on the basis of two criteria, namely, D α , r , ϑ control system provides stabilization of the vertical plasma position on the real-time digital control testbed. [ABSTRACT FROM AUTHOR]

Precise motion control remains one of the most important problems in modern technology. It is especially difficult in the case of two-mass systems with flexible coupling if only the motor position and velocity are measured. We propose a new methodology of control system design in this situation. The concept is founded on a robust observer design, based on a linear matrix inequality (LMI) solution. The observer cooperates with the original nonlinear controller. The presented approach allows us to solve the position tracking problem for a two-mass drive, with unknown parameters, in the presence of disturbances (for instance, nonlinear friction-like torques) acting on both ends of the flexible shaft. Under this set of assumptions, the problem was never solved previously. The closed-loop system stability is investigated, and the uniform ultimate boundedness of state estimation errors and tracking errors is proven using Lyapunov techniques. Numerical properties of the design procedure and characteristic features of the observer, controller, and closed-loop system are demonstrated by several examples. [ABSTRACT FROM AUTHOR]

This article presents a novel solution for adaptive output feedback of uncertain nonlinear systems; it uses nonlinear controller and observer structures to drive a time‐varying function as a Lyapunov one, thus guaranteeing asymptotic stability of the system states and observation error. Exact convex modeling of available terms and polytopic embedding of unavailable ones in the Lyapunov function dynamics, allow linear matrix inequalities to be used, thus overcoming former difficulties over the non‐convex nature of the problem. Moreover, the proposal incorporates a recently appeared factorization to get rid of approximate solutions based on Lipschitz bounds and persistence of excitation. The methodology is successfully put at test against related works in a variety of examples. [ABSTRACT FROM AUTHOR]

Restricting transient peaks of contact force in teleoperation systems is undeniably vital, specially in critical applications such as telesurgery. This issue, however, has still remained unsolved in the literature. In order to address this problem, we propose an impedance control scheme using optimal L 1 theory for teleoperation systems encompassing asymmetric randomly time-varying delays and model uncertainties. To this end, an L 1-based state-feedback compensator is designed employing linear matrix inequalities, aiming at minimizing the desired impedance error subjected to human force as exogenous disturbance. A simulation is ultimately conducted in comparison with the sliding-mode-based impedance controller. The results validate that the proposed controller is able to keep the integral of impedance error within the desired bound and, thus, improves the transient response. This is, however, at the expense of imposing a steady-state error for the integral of impedance error, which is normally made zero by the sliding-mode controller. [ABSTRACT FROM AUTHOR]

This paper proposes a new robust output-feedback adaptive event-triggered control (AETC) method for linear systems with parametric uncertainties. The proposed event-triggered mechanism (ETM) is obtained based on the L 2 stability condition. In this paper, two design approaches are presented, the emulation approach (pre-designed control gain) and the co-design approach. In the latter, the event-triggering law and the output-feedback controller are designed simultaneously to have a more efficient control system. The proposed adaptive event-triggered mechanism (AETM) in both approaches leads to an increase in the average of inter-event times based on linear matrix inequalities (LMIs). Consequently, in the proposed methods, the stability of the event-based system is ensured, the Zeno phenomenon is avoided, the feasibility margin and the quality of the response are well maintained, and the number of samplings is reduced, considerably. Finally, to indicate the capability of the proposed methods, two numerical simulations are presented. [ABSTRACT FROM AUTHOR]

An analysis and controller design of double-input dc–dc converter (DIDDC) is introduced in this article. This converter is integrated with buck and boost converters at the front-end and a charge pump on the back-end. Salient features of this topology are as follows: (i) ripple content is low in source currents, (ii) both the dc sources are connected through an inductor, which gives rise to a smooth source current waveform, (iii) both the sources supply power to load either in standalone or simultaneously together, and (iv) two control–loops (one for source current regulation, while the second one for load voltage regulation) are sufficient enough to ensure power transfer/management from dc sources to load. To ensure power management on the input dc sources while keeping a stable closed-loop converter system, a multivariable diagonal controller is designed. The first diagonal controller performs the load voltage regulation task, while the second controller regulates input of source-2 dc current. From the control point of view, the double-input single-output converter becomes a two-input two-output control problem and exhibits control–loop interactions due to the power flow from two different sources to load through common elements. The impact of off-diagonal elements’ interactions is accounted by using decouplers. The H∞ robust control theory and linear matrix inequality (LMI) principles are adopted to design reliable controllers. The structured controller of fixed order (PID) is designed by enforcing the necessary type LMIs. To demonstrate the feasibility and effectiveness of multivariable controllers of the DIDDC, a 60/24 V to 48 V, 150 W, 50 kHz topology prototype is constructed, and the power management aspects are investigated experimentally. Load voltage regulation, source current regulation, load sharing on the input dc sources, and power management aspects of LMI-based controllers were tested extensively for all possible disturbances. In all these test cases, the closed-loop double-input converter system is stable and robust in rejecting a variety of disturbances created. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system. [ABSTRACT FROM AUTHOR]

This paper is concerned with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) control having filtered derivative terms to achieve optimal linear quadratic performance for a class of linear uncertain MIMO systems with norm-bounded time-varying uncertainties. A necessary and sufficient condition for existence of the PID controller is obtained in terms of rank constrained linear matrix inequalities (LMIs). Using an existing penalty-function-based approximation for matrix rank minimization, an algorithm is proposed to solve these rank constrained LMIs and find PID gains. A suitable numerical example is considered to show the efficacy of the proposed approach in ensuring robust performance as compared to the existing ones. The proposed algorithm is also tested on several benchmark examples and found to be computationally much more efficient than some well-known methods. [ABSTRACT FROM AUTHOR]

The essential prerequisites for secure customer service are power system stability and reliability. This work shows how to construct a robust switching control for studying power system load changes using an invariant ellipsoid method. Furthermore, the suggested control ensures stability when the system is subjected to random stochastic external disturbances, and functions randomly in two conditions: normal and contingency. The extreme (least) reliability state is chosen as the most severe scenario (corresponding to a transmission line outage). As a two-state Markov random chain, the transition probabilities are utilized to simulate the switching between normal and contingency modes (or processes). To characterize the dynamics of the studied system, a stochastic mathematical model is developed. The effect of stochastic disturbances and random normal/contingency operations is taken into account during the design stage. For a stochastic power system, a novel excitation control is designed. The attractive ellipsoid approach and linear matrix inequalities (LMIs) optimization are used to build the best two-controller gains. Therefore, the proposed modeling/design technique can be employed for the power system under load changes, stochastic topological changes, and random disturbances. Finally, the system's random dynamics simulation indicates the effectiveness of the designed control law. [ABSTRACT FROM AUTHOR]